"On Smoothness of the Green Function"

By

**Abstract: **If a compact set K is regular with respect to the Dirichlet problem,
then the Green function g of the complement of K with pole at infinity is
continuous throughout the complex plane. We discuss character of continuity of
g near the boundary of the domain, review new results by Totik and Andrievskii
concerning compact sets with optimal smoothness of g and describe the
smoothness of the Green functions for the complement of rarefied Cantor-type
sets in terms of the function that gives the logarithmic measure of sets.
Markov's constants of the corresponding sets are evaluated. The result is joint
with M.Altun.

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Tea and cookies will be served before the
seminar.

**Date: ****Wednesday,
April 22, 2009**

**Time: ****14.40**

**Place: ****Mathematics Seminar Room, SA-141**